Journal of Function Spaces http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. New Type of Sturm-Liouville Problems in Associated Hilbert Spaces Wed, 16 Apr 2014 08:21:30 +0000 http://www.hindawi.com/journals/jfs/2014/606815/ We introduce a new type of discontinuous Sturm-Liouville problems, involving an abstract linear operator in equation. By suggesting own approaches we define some new Hilbert spaces to establish such properties as isomorphism, coerciveness, and maximal decreasing of resolvent operator with respect to spectral parameter. Then we find sufficient conditions for discreteness of the spectrum and examine asymptotic behaviour of eigenvalues. Obtained results are new even for continuous case, that is, without transmission conditions. O. Sh. Mukhtarov and K. Aydemir Copyright © 2014 O. Sh. Mukhtarov and K. Aydemir. All rights reserved. Stability of Pexider Equations on Semigroup with No Neutral Element Thu, 10 Apr 2014 12:09:23 +0000 http://www.hindawi.com/journals/jfs/2014/153610/ Let be a commutative semigroup with no neutral element, a Banach space, and the set of complex numbers. In this paper we prove the Hyers-Ulam stability for Pexider equation for all , where . Using Jung’s theorem we obtain a better bound than that usually obtained. Also, generalizing the result of Baker (1980) we prove the superstability for Pexider-exponential equation for all , where . As a direct consequence of the result we also obtain the general solutions of the Pexider-exponential equation for all , a closed form of which is not yet known. Jaeyoung Chung Copyright © 2014 Jaeyoung Chung. All rights reserved. On the Graph of Solution Mappings of Variational Inequalities Problems Wed, 09 Apr 2014 13:29:26 +0000 http://www.hindawi.com/journals/jfs/2014/853106/ This paper shows the property of homeomorphism between the space of monotone variational inequalities problems and the graph of their solution mappings. Qi-Qing Song Copyright © 2014 Qi-Qing Song. All rights reserved. An Exact Solution of the Binary Singular Problem Wed, 09 Apr 2014 07:31:00 +0000 http://www.hindawi.com/journals/jfs/2014/580497/ Singularity problem exists in various branches of applied mathematics. Such ordinary differential equations accompany singular coefficients. In this paper, by using the properties of reproducing kernel, the exact solution expressions of dual singular problem are given in the reproducing kernel space and studied, also for a class of singular problem. For the binary equation of singular points, I put it into the singular problem first, and then reuse some excellent properties which are applied to solve the method of solving differential equations for its exact solution expression of binary singular integral equation in reproducing kernel space, and then obtain its approximate solution through the evaluation of exact solutions. Numerical examples will show the effectiveness of this method. Baiqing Sun, Kun Tang, Hongmei Zhang, and Shan Xiong Copyright © 2014 Baiqing Sun et al. All rights reserved. Nonlocal Variational Principles with Variable Growth Mon, 07 Apr 2014 12:09:46 +0000 http://www.hindawi.com/journals/jfs/2014/435247/ This paper is concerned with the functional defined by , where is a regular open bounded set and is a real-valued function with variable growth. After discussing the theory of Young measures in variable exponent Sobolev spaces, we study the weak lower semicontinuity and relaxation of . Yongqiang Fu and Miaomiao Yang Copyright © 2014 Yongqiang Fu and Miaomiao Yang. All rights reserved. Marcinkiewicz Integrals on Weighted Weak Hardy Spaces Thu, 03 Apr 2014 08:31:47 +0000 http://www.hindawi.com/journals/jfs/2014/765984/ We prove that, under the condition , Marcinkiewicz integral is bounded from weighted weak Hardy space to weighted weak Lebesgue space for , where belongs to the Muckenhoupt weight class. We also give weaker smoothness condition assumed on Ω to imply the boundedness of from to . Yue Hu and Yueshan Wang Copyright © 2014 Yue Hu and Yueshan Wang. All rights reserved. The Commutators of Fractional Integrals on Generalized Herz Spaces Thu, 03 Apr 2014 08:24:01 +0000 http://www.hindawi.com/journals/jfs/2014/428493/ Let be the fractional integral, and let . We will obtain the weighted estimates for the commutator on the generalized Herz spaces. Yue Hu, Yuexiang He, and Yueshan Wang Copyright © 2014 Yue Hu et al. All rights reserved. Malliavin Derivatives in Spaces with Variable Exponents Thu, 03 Apr 2014 08:21:00 +0000 http://www.hindawi.com/journals/jfs/2014/198060/ Spaces with variable exponents and are introduced. After discussing some approximation results of , Sobolev spaces on H with variable exponents are introduced. At last, we define Malliavin derivatives in and discuss some properties of Malliavin derivatives in . Bochi Xu, Yongqiang Fu, and Boping Tian Copyright © 2014 Bochi Xu et al. All rights reserved. -Tuplet Coincidence Point Theorems in Intuitionistic Fuzzy Normed Spaces Sun, 30 Mar 2014 14:26:07 +0000 http://www.hindawi.com/journals/jfs/2014/821342/ For an arbitrary n positive integer, we investigate the existence of n-tuplet coincidence points in intuitionistic fuzzy normed space. Results of the paper are more general than those of the coupled and the tripled fixed point works in intuitionistic fuzzy normed space. Müzeyyen Ertürk and Vatan Karakaya Copyright © 2014 Müzeyyen Ertürk and Vatan Karakaya. All rights reserved. Norm Comparison Estimates for the Composite Operator Sun, 30 Mar 2014 13:50:41 +0000 http://www.hindawi.com/journals/jfs/2014/943986/ This paper obtains the Lipschitz and BMO norm estimates for the composite operator applied to differential forms. Here, is the Hardy-Littlewood maximal operator, and is the potential operator. As applications, we obtain the norm estimates for the Jacobian subdeterminant and the generalized solution of the quasilinear elliptic equation. Xuexin Li, Yong Wang, and Yuming Xing Copyright © 2014 Xuexin Li et al. All rights reserved. Solution of Nonlinear Partial Differential Equations by New Laplace Variational Iteration Method Wed, 26 Mar 2014 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2014/790714/ The aim of this study is to give a good strategy for solving some linear and nonlinear partial differential equations in engineering and physics fields, by combining Laplace transform and the modified variational iteration method. This method is based on the variational iteration method, Laplace transforms, and convolution integral, introducing an alternative Laplace correction functional and expressing the integral as a convolution. Some examples in physical engineering are provided to illustrate the simplicity and reliability of this method. The solutions of these examples are contingent only on the initial conditions. Eman M. A. Hilal and Tarig M. Elzaki Copyright © 2014 Eman M. A. Hilal and Tarig M. Elzaki. All rights reserved. Optimal Couples of Rearrangement Invariant Spaces for Generalized Maximal Operators Wed, 19 Mar 2014 11:43:42 +0000 http://www.hindawi.com/journals/jfs/2014/647123/ The optimal couples of rearrangement invariant spaces for boundedness of a generalized maximal operator, associated with a quasiconcave function, have been characterized in terms of certain indices connected with rearrangement invariant spaces and quasiconcave functions. Irshaad Ahmed and Waqas Nazeer Copyright © 2014 Irshaad Ahmed and Waqas Nazeer. All rights reserved. Isometric Reflection Vectors and Characterizations of Hilbert Spaces Tue, 18 Mar 2014 12:05:30 +0000 http://www.hindawi.com/journals/jfs/2014/634082/ A known characterization of Hilbert spaces via isometric reflection vectors is based on the following implication: if the set of isometric reflection vectors in the unit sphere of a Banach space has nonempty interior in , then is a Hilbert space. Applying a recent result based on well-known theorem of Kronecker from number theory, we improve this by substantial reduction of the set of isometric reflection vectors needed in the hypothesis. Donghai Ji and Senlin Wu Copyright © 2014 Donghai Ji and Senlin Wu. All rights reserved. Another Class of Distances and Continuous Quasi-Distances in Product Spaces Tue, 18 Mar 2014 06:03:06 +0000 http://www.hindawi.com/journals/jfs/2014/861362/ We construct a class of continuous quasi-distances in a product of metric spaces and show that, generally, when the parameter (as shown in the paper) is positive, is a distance and when , is only a continuous quasi-distance, but not a distance. It is remarkable that the same result in relation to the sign of was found for two other classes of continuous quasi-distances (see Peppo (2010a, 2010b) and Peppo (2011)). This conclusion is due to the fact that is a product space. For the purposes of our main result, a notion of density in metric spaces is introduced. Catherine Peppo Copyright © 2014 Catherine Peppo. All rights reserved. The Boundedness of the Hardy-Littlewood Maximal Operator and Multilinear Maximal Operator in Weighted Morrey Type Spaces Sun, 16 Mar 2014 08:41:25 +0000 http://www.hindawi.com/journals/jfs/2014/648251/ The aim of this paper is to prove the boundedness of the Hardy-Littlewood maximal operator on weighted Morrey spaces and multilinear maximal operator on multiple weighted Morrey spaces. In particular, the result includes the Komori-Shirai theorem and the Iida-Sato-Sawano-Tanaka theorem for the Hardy-Littlewood maximal operator and multilinear maximal function. Takeshi Iida Copyright © 2014 Takeshi Iida. All rights reserved. The Cores for Fuzzy Games Represented by the Concave Integral Thu, 13 Mar 2014 15:42:55 +0000 http://www.hindawi.com/journals/jfs/2014/318764/ We propose a new fuzzy game model by the concave integral by assigning subjective expected values to random variables in the interval . The explicit formulas of characteristic functions which are determined by coalition variables are discussed in detail. After illustrating some properties of the new game, its fuzzy core is defined; this is a generalization of crisp core. Moreover, we give a further discussion on the core for the new games. Some notions and results from classical games are extended to the model. The nonempty fuzzy core is given in terms of the fuzzy convexity. Our results develop some known fuzzy cooperative games. Jinhui Pang and Shujin Li Copyright © 2014 Jinhui Pang and Shujin Li. All rights reserved. Wick Analysis for Bernoulli Noise Functionals Wed, 12 Mar 2014 08:44:39 +0000 http://www.hindawi.com/journals/jfs/2014/727341/ A Gel’fand triple is constructed of functionals of , where is an appropriate Bernoulli noise on a probability space . Characterizations are given to both and . It is also shown that a Wick-type product can be defined on and moreover forms a commutative algebra with the product. Finally, a transform named -transform is defined on and its continuity as well as other properties are examined. Caishi Wang and Jihong Zhang Copyright © 2014 Caishi Wang and Jihong Zhang. All rights reserved. Circle-Uniqueness of Pythagorean Orthogonality in Normed Linear Spaces Tue, 11 Mar 2014 13:38:09 +0000 http://www.hindawi.com/journals/jfs/2014/634842/ We introduce the circle-uniqueness of Pythagorean orthogonality in normed linear spaces and show that Pythagorean orthogonality is circle-unique if and only if the underlying space is strictly convex. Further related results providing more detailed relations between circle-uniqueness of Pythagorean orthogonality and the shape of the unit sphere are also presented. Senlin Wu, Xinjian Dong, and Dan Wang Copyright © 2014 Senlin Wu et al. All rights reserved. Multiplicity of Solutions for an Elliptic Problem with Critical Sobolev-Hardy Exponents and Concave-Convex Nonlinearities Thu, 06 Mar 2014 00:00:00 +0000 http://www.hindawi.com/journals/jfs/2014/180105/ We study the existence of multiple solutions for the following elliptic problem: We prove that if , then there is a , such that for any , the above mentioned problem possesses infinitely many weak solutions. Our result generalizes a similar result (Azorero and Alonso, 1991). Juan Li and Yuxia Tong Copyright © 2014 Juan Li and Yuxia Tong. All rights reserved. A Remark on the Homogeneity of Isosceles Orthogonality Sun, 02 Mar 2014 11:13:24 +0000 http://www.hindawi.com/journals/jfs/2014/876015/ Inspired by the definition of homogeneous direction of isosceles orthogonality, we introduce the notion of almost homogeneous direction of isosceles orthogonality and show that, surprisingly, these two notions coincide. Several known characterizations of inner products are improved. Chan He and Dan Wang Copyright © 2014 Chan He and Dan Wang. All rights reserved. Arzela-Ascoli Theorem for Demi-Linear Mappings Sun, 02 Mar 2014 11:12:13 +0000 http://www.hindawi.com/journals/jfs/2014/679825/ The Arzela-Ascoli theorem for demi-linear mappings is established. Some conclusions about preserving totally bounded sets are also obtained. Qiang Lei and Aihong Chen Copyright © 2014 Qiang Lei and Aihong Chen. All rights reserved. Anisotropic, Mixed-Norm Lizorkin-Triebel Spaces and Diffeomorphic Maps Sun, 02 Mar 2014 10:24:57 +0000 http://www.hindawi.com/journals/jfs/2014/964794/ This paper gives general results on invariance of anisotropic Lizorkin-Triebel spaces with mixed norms under coordinate transformations on Euclidean space, open sets, and cylindrical domains. J. Johnsen, S. Munch Hansen, and W. Sickel Copyright © 2014 J. Johnsen et al. All rights reserved. The Identical Estimates of Spectral Norms for Circulant Matrices with Binomial Coefficients Combined with Fibonacci Numbers and Lucas Numbers Entries Thu, 27 Feb 2014 16:06:01 +0000 http://www.hindawi.com/journals/jfs/2014/672398/ Improved estimates for spectral norms of circulant matrices are investigated, and the entries are binomial coefficients combined with either Fibonacci numbers or Lucas numbers. Employing the properties of given circulant matrices, this paper improves the inequalities for their spectral norms, and gets corresponding identities of spectral norms. Moreover, by some well-known identities, the explicit identities for spectral norms are obtained. Some numerical tests are listed to verify the results. Jianwei Zhou Copyright © 2014 Jianwei Zhou. All rights reserved. An Odd Rearrangement of () Wed, 26 Feb 2014 09:13:20 +0000 http://www.hindawi.com/journals/jfs/2014/787840/ We introduce an odd rearrangement defined by , , where is a decreasing rearrangement of the measurable function . With the help of this odd rearrangement, we show that for each , there exists a such that , where is an distribution function of . Moreover, we study the boundedness of singular integral operators when they are restricted to odd rearrangement of , and we give some results on Hilbert transform. Zheng Wang and Jiecheng Chen Copyright © 2014 Zheng Wang and Jiecheng Chen. All rights reserved. Stability for Functional Equation of Mixed Type in Non-Archimedean Normed Spaces Tue, 25 Feb 2014 07:19:30 +0000 http://www.hindawi.com/journals/jfs/2014/919646/ We take into account the stability of the following functional equation in non-Archimedean normed spaces. Ick-Soon Chang and Yang-Hi Lee Copyright © 2014 Ick-Soon Chang and Yang-Hi Lee. All rights reserved. Eigenvalues of a Class of Singular Boundary Value Problems of Impulsive Differential Equations in Banach Spaces Sun, 23 Feb 2014 10:14:17 +0000 http://www.hindawi.com/journals/jfs/2014/720494/ This paper is devoted to investigating the eigenvalue problems of a class of nonlinear impulsive singular boundary value problem in Banach spaces: ; where denotes the zero element of Banach space, , , , is a parameter, and may be singular at and . The arguments are mainly based upon the theory of fixed point index, measure of noncompactness, and the special cone, which is constructed to overcome the singularity. Daliang Zhao and Yansheng Liu Copyright © 2014 Daliang Zhao and Yansheng Liu. All rights reserved. The Arens Algebras of Vector-Valued Functions Sun, 23 Feb 2014 09:38:27 +0000 http://www.hindawi.com/journals/jfs/2014/248925/ A class of Arens algebras of vector Banach algebra valued functions is considered. It is shown that Arens algebra of vector-valued functions is complete locally convex metrizable algebra. I. G. Ganiev and O. I. Egamberdiev Copyright © 2014 I. G. Ganiev and O. I. Egamberdiev. All rights reserved. Approximation on the Quadratic Reciprocal Functional Equation Thu, 20 Feb 2014 08:19:14 +0000 http://www.hindawi.com/journals/jfs/2014/532463/ The quadratic reciprocal functional equation is introduced. The Ulam stability problem for an -quadratic reciprocal mapping between nonzero real numbers is solved. The Găvruţa stability for the quadratic reciprocal functional equations is established as well. Abasalt Bodaghi and Sang Og Kim Copyright © 2014 Abasalt Bodaghi and Sang Og Kim. All rights reserved. Geometry of Banach Spaces, Operator Theory, and Their Applications Tue, 18 Feb 2014 12:33:59 +0000 http://www.hindawi.com/journals/jfs/2014/635649/ Genqi Xu, Ji Gao, Peide Liu, and Satit Saejung Copyright © 2014 Genqi Xu et al. All rights reserved. Endpoint Estimates for Fractional Hardy Operators and Their Commutators on Hardy Spaces Tue, 18 Feb 2014 12:05:32 +0000 http://www.hindawi.com/journals/jfs/2014/272864/ bounds of fractional Hardy operators are obtained. Moreover, the estimates for commutators of fractional Hardy operators on Hardy spaces are worked out. It is also proved that the commutators of fractional Hardy operators are mapped from the Herz-type Hardy spaces into the Herz spaces. The estimates for multilinear commutators of fractional Hardy operators are also discussed. Jiang Zhou and Dinghuai Wang Copyright © 2014 Jiang Zhou and Dinghuai Wang. All rights reserved.